Bourgain’s discretization theorem

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Bourgain’s Discretization Theorem

Bourgain’s discretization theorem asserts that there exists a universal constant C ∈ (0,∞) with the following property. Let X,Y be Banach spaces with dimX = n. Fix D ∈ (1,∞) and set δ = e−nCn . Assume that N is a δ-net in the unit ball of X and that N admits a bi-Lipschitz embedding into Y with distortion at most D. Then the entire space X admits a bi-Lipschitz embedding into Y with distortion ...

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ژورنال

عنوان ژورنال: Annales de la faculté des sciences de Toulouse Mathématiques

سال: 2012

ISSN: 0240-2963

DOI: 10.5802/afst.1352